API RP 1111 — Pipeline Wall Thickness Assessment

Moment-Tension Interaction Report

OD 273.05 mm
WT 21.44 mm
Grade X65
Governing Propagation — 0.522 PASS

Executive Summary

PASS
Overall VerdictPASS — 3/3 checks passed
Governing CheckPropagation
Governing Utilisation0.522
Margin47.8%
Design CodeAPI RP 1111
PipeOD 273.05 mm × WT 21.44 mm, X65
PressurePi = 20.00 MPa, Pe = 10.00 MPa (Pnet = 10.00 MPa)

1. Pressure-Only Checks (API RP 1111)

Independent of bending moment and tension — these set the baseline utilisation.

Check Capacity (MPa) Design Factor Allowable (MPa) Demand (MPa) Utilisation Status
Burst
Sec 4.3.1.1
75.260.7254.1910.000.185PASS
Collapse
Sec 4.3.2
67.020.8053.6110.000.187PASS
Propagation
Sec 4.3.3
23.960.8019.1710.000.522PASS

2. Capacity Limits by Operating Condition

Pure tension and pure bending limits at util = 1.0 for each API RP 1111 operating condition. Tension limits are asymmetric due to hoop stress interaction: positive tension (pipe stretching) is more favourable than compression when net internal pressure is positive.

Condition fd T+ (kN) T (kN) Mallow (kN·m)
Normal Operating0.725864.3-4954.6289.2
Installation0.806477.5-5567.8325.1
Extreme0.967700.9-6791.2396.5
Survival1.008006.3-7096.6414.3

2a. Pressure Sensitivity — Effect of Internal Pressure

Capacity limits recomputed at baseline, +50%, and +100% internal pressure. Higher hoop stress shrinks all envelopes and increases the asymmetry between positive and negative tension limits.

Pi (MPa)σh (MPa)ConditionfdT+ (kN)T (kN)Mallow (kN·m)
2053.7Normal Operating0.725864.3-4954.6289.2
Installation0.806477.5-5567.8325.1
Extreme0.967700.9-6791.2396.5
Survival1.008006.3-7096.6414.3
30 (+50%)107.4Normal Operating0.726144.3-4324.8252.5
Installation0.806775.7-4956.3289.4
Extreme0.968026.1-6206.7362.4
Survival1.008336.8-6517.5380.5
40 (+100%)161.0Normal Operating0.726293.8-3564.7208.1
Installation0.806959.8-4230.7247.0
Extreme0.968259.4-5530.3322.9
Survival1.008579.8-5850.7341.6

3. Combined Loading — Von Mises Interaction

The API RP 1111 combined check evaluates the Von Mises equivalent stress: σvm = √(σL² − σL·σh + σh²) ≤ fd·SMYS

The contour plot below maps utilisation across the bending moment vs. tension envelope. The bold black contour at util = 1.0 is the acceptance boundary; the dashed contour at 0.8 marks a typical design target.

4. Allowable Bending Envelope

Each curve traces the maximum allowable bending moment as a function of applied tension, at util = 1.0 for that operating condition. The Normal Operating envelope (innermost) is the most conservative; the Survival envelope (outermost) represents the full yield limit.

Envelope Data — Tension vs Allowable Bending Moment

Tension (kN)Normal Operating
Mallow (kN·m)
Installation
Mallow (kN·m)
Extreme
Mallow (kN·m)
Survival
Mallow (kN·m)
-49550.00.00.00.0
-441431.635.242.344.1
-387363.170.484.688.2
-333294.8105.5126.9132.3
-2791126.3140.7169.2176.3
-2250157.9175.8211.5220.4
-1709189.5211.0253.8264.6
-1168221.1246.1296.1308.6
-627252.7281.3338.4352.7
-86284.2316.5380.8396.8
455315.8351.6423.1440.9
996284.2316.5380.8396.8
1537252.7281.3338.4352.7
2078221.1246.1296.1308.6
2619189.5211.0253.8264.6
3160157.9175.8211.5220.4
3701126.3140.7169.2176.3
424194.8105.5126.9132.3
478263.170.484.688.2
532331.635.242.344.1
58640.00.00.00.0

5. Key Points Summary

Utilisation at selected engineering reference points on the M–T plane.

Point T (kN) M (kN·m) T / Ty M / Mp Utilisation Margin Status
Pressure only (origin)0.00.00.0000.0000.16683.4%PASS
T = 0.5 T_y3796.20.00.5000.0000.62837.2%PASS
T = 0.8 T_y6073.90.00.8000.0001.0380.0%FAIL
T = 1.0 T_y7592.40.01.0000.0001.3140.0%FAIL
M = 0.5 M_p0.0304.80.0000.5001.0480.0%FAIL
M = 0.8 M_p0.0487.60.0000.8001.6180.0%FAIL
M = 1.0 M_p0.0609.50.0001.0001.9980.0%FAIL
T = 0.5 T_y + M = 0.5 M_p3796.2304.80.5000.5001.5730.0%FAIL
T = 0.5 T_y + M = 0.8 M_p3796.2487.60.5000.8002.1440.0%FAIL
T = 0.8 T_y + M = 0.5 M_p6073.9304.80.8000.5001.9880.0%FAIL

6. Input Data

Pipe Geometry

Outer Diameter (OD)273.05 mm
Wall Thickness (WT)21.44 mm
Inner Diameter (ID)230.17 mm
D/t Ratio12.7
Corrosion Allowance1.00 mm

Material Properties

GradeX65
SMYS448.00 MPa
SMTS531.00 MPa
Young’s Modulus207 GPa
Poisson’s Ratio0.30
Fabrication TypeSeamless

Design Conditions

Internal Pressure (Pi)20.00 MPa
External Pressure (Pe)10.00 MPa
Net Pressure (Pnet)10.00 MPa
Hoop Stress (σh)53.68 MPa

Derived Section Properties

Cross-sectional Area (A)169.47 cm²
Section Modulus (Z)989.46 cm³
Second Moment of Area (I)13508.60 cm⁴
Yield Tension (Ty)7592.4 kN
Plastic Moment (Mp)609.5 kN·m